Solutions of some functional-integral equations in Banach algebra

Bana, J.; Sadarangani, Kishin

doi:10.1016/s0895-7177(03)90084-7

Cited by 57 publications

(28 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence, estimate (4) proves that operator T is continuous on B r0 . Moreover, we show that operator T satisfies (2) with respect to measure of noncompactness ω 0 given by (3). To do this, we choose a fixed arbitrary ε > 0.…”

Section: S Y(γ(s)))ds Y (β(T))mentioning

confidence: 95%

“…Many articles in the field of functional integral equations give different conditions for the existence of the solutions of some nonlinear functional integral equations. A. Aghajani and Y. Jalilian in [1], J. Banaś and K. Sadarangani in [3], Zeqing Liu et al in [11] and so on are some of these. The following equation has been considered in [6] :…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the solutions of a class of nonlinear functional integral equations in space C [0,a]

Özdemır

Çakan

2015

JMA

View full text Add to dashboard Cite

On the solutions of a class of nonlinear functional integral equations in space C [0, a] IsmetÖzdemir andÜmit Ç akanAbstract: The principal aim of this paper is to give sufficient conditions for solvability of a class of some nonlinear functional integral equations in the space of continuous functions defined on interval [0, a]. The main tool used in our study is associated with the technique of measures of noncompactness. We give also some examples satisfying the conditions of our main theorem but not satisfying the conditions in [8].

show abstract

Section: S Y(γ(s)))ds Y (β(T))mentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

On the solutions of a class of nonlinear functional integral equations in space C [0,a]

Özdemır

Çakan

2015

JMA

View full text Add to dashboard Cite

show abstract

“…[6,7,11,12,18,19]). We will use the technique associated with measures of noncompactness and some fixed point theorems [5].…”

Section: Introductionmentioning

confidence: 99%

Measures of Noncompactness in a Banach Algebra and Their Applications

Dudek¹

2017

JMA

View full text Add to dashboard Cite

In this paper we study the existence of solutions of a nonlinear quadratic integral equation of fractional order. This equation is considered in the Banach space of real functions defined, continuous and bounded on the real half axis. Additionally, using the technique of measures of noncompactness we obtain some characterization of considered integral equation. We provide also an example illustrating the applicability of our approach.

show abstract

“…In recent years, many authors have focused on the resolution of Eq. (1.1) and obtained a lot of valuable results (see for example [3][4][5][6]9,[11][12][13][14]16] and the references therein). These studies were mainly based on the convexity of the bounded domain, the celebrate Schauder fixed point theorem [16] and properties of operators A, B and C (cf.…”

Section: Introductionmentioning

confidence: 99%